The present invention relates to a method and apparatus for measuring the resistivity of formations having a borehole passing therethrough, and is particularly applicable to the error-prone situation of measuring the resistivity of a conducting layer situated beneath a layer of high resistivity and of considerable thickness, with the bottom end or "shoe" of the casing being situated at the bottom of the thick layer.
Conventional apparatus for resistivity logging is Schlumberger's Dual Laterolog (DLT) described in particular in U.S. Pat. Nos. 3,772,589 (Scholberg) and 4,291,267 (Bonnet). This apparatus comprises a sonde suspended from an electric cable by means of an insulating cable, with the sonde having an elongate shape suitable for displacement inside boreholes. The sonde includes a central electrode A.sub.0 emitting a current I.sub.0 into the formation, and focusing electrodes (A.sub.1, A'.sub.1 and A.sub.2, A'.sub.2) disposed symmetrically on either side of the central electrode and intended to produce focussing currents which ensure that the radial penetration of the current I.sub.0 into the formation is appropriate. The sonde also includes one or more potential-measuring electrodes M placed between the electrodes A.sub.0 and A.sub.1 or A'.sub.1. In addition to the sonde, the apparatus includes a reference potential electrode N situated on the insulating cable or at its top end where it joins the electric cable, and a current return electrode B placed on the surface. The resistivity value provided by this apparatus is the apparent resistivity: EQU R.sub.a =K(V.sub.M -V.sub.N)/I.sub.0
where K is a constant called the geometric factor, V.sub.M is the potential of the sonde as measured using the electrodes M, V.sub.N is the reference potential, and I.sub.0 is the current emitted by the electrode A.sub.0.
In the above-mentioned apparatus, the emitted current is an alternating current. In order to obtain measurements simultaneously at different investigation depths, two different frequencies are used: a low frequency (35 Hz) for the deeper measurement called LLd; and a higher frequency (280 Hz) for the shallower measurement called LLs. However the present description relates only to the deeper measurement which is the only one requiring a return electrode on the surface.
Under special conditions, the measurement of the resistivity of a formation is subject to an error known as the Groningen effect. Reference may be made to US Pat. No. 4,335,353 (Lacour-Gayet) on this subject. This effect occurs when a layer of great thickness and high resistivity lies over a more conductive formation whose resistivity is to be evaluated. It can be explained by two factors.
Firstly, current is transferred between the formation and the conducting armor of the cable. According to transmission line theory, this transfer to the core of the cable takes place over a characteristic length (L.sub.c) given by L.sub.c =(R.sub.s /R.sub.c).sup.1/2, where R.sub.s is the resistivity of the formation situated around the cable core, and R.sub.c is the resistance of the cable per unit length. It can be seen that the characteristic length L.sub.c is long if the resistivity R.sub.s of the formation around the core is high. In practice, the presence of the core has the effect of deforming equipotential surfaces so that instead of being orthogonal to the borehole, they slope towards it. As a result, the potential of the reference electrode N, instead of being equal to the potential of a zone of formation situated at the same level as and at a significant distance from the borehole in a radial direction, actually corresponds to the potential at a shallower level (i.e. a level closer to the surface), offset by a length Lc relative to the level of the reference electrode.
Secondly, current lines going towards the surface are concentrated by the skin effect into a cylinder centered on the cable. This cylinder is analogous to a coaxial cable and has a resistance R.sub.e per unit length which is independent of the resistivity of the formation. This results in a drop in potential per unit length of .DELTA.V=R.sub.e /I.sub.T where I.sub.T is the total current emitted by the apparatus. Since the length to be taken into consideration is the above-mentioned characteristic length L.sub.c, the error in the reference potential is: EQU .DELTA.V/L.sub.c =R.sub.e /I.sub.T /(R.sub.s /R.sub.c).sup.1/2
and the resulting measurement error is EQU .DELTA.R.sub.a =K/R.sub.e /(I.sub.T /I.sub.0)/(R.sub.s /R.sub.c).sup.1/2
using typical values for the various parameters, this gives EQU .DELTA.R.sub.a .perspectiveto.0.01 R.sub.s.sup.1/2
It is observed that the error may become considerable when the resistivity R.sub.s of the layer surrounding the reference electrode N is high. The error is of the order of 1 ohm-m for a resistivity R.sub.s of the order of 10000 ohm-m. Consequently, if the formation at the sonde is conductive (e.g. if its apparent resistivity R.sub.a is of the order of 1 ohm-m), then a very large relative error .DELTA.R.sub.a /R.sub.a occurs.
Above-mentioned U.S. Pat. No. 4,335,353 describes a technique for correcting this error based on measuring the component of the potential that is in quadrature relative to the total current I.sub.T. This method gives satisfaction so long as the high resistivity layer is situated far away from the cased section of the borehole.
However, this method is inadequate when the borehole includes a cased section and the casing shoe (i.e. the bottom end thereof) is situated over the boundary between the conducting layer and the high resistivity layer. Under such circumstances, because of the skin effect in the tubing (generally made of steel), and therefore highly conductive, the current emitted by the measurement device is concentrated in a thin (a few millimeters thick) portion of the casing wall, on the inside of the casing and with a high current gradient occurring towards the casing shoe which then acts as the return electrode instead of the electrode on the surface. This gives rise to an error in the reference potential which may be ten to twenty times greater than the error that would occur in the absence of any casing.
One object of the invention is to provide a technique capable of correcting the error relating to the reference potential, including under the difficult circumstances of the casing shoe being situated at the bottom of the high resistivity layer.